1. Field of the Invention
This invention relates generally to communication systems, and, more particularly, to wireless communication sequences.
2. Description of the Related Art
Wireless communication systems typically include one or more base stations or access points for providing wireless connectivity to mobile units in a geographic area (or cell) associated with each base station or access point. Mobile units and base stations communicate by transmitting modulated radiofrequency signals over a wireless communication link, or air interface. The air interface includes downlink (or forward link) channels for transmitting information from the base station to the mobile unit and uplink (or reverse link) channels for transmitting information from the mobile unit to the base station. The uplink and downlink channels are typically divided into data channels, random access channels, broadcast channels, paging channels, signaling channels, control channels, and the like. The uplink and downlink channels may be shared or dedicated.
Mobile units can initiate communication with the base station by transmitting a message on one or more of the random access channels (RACHs). Uplink random access messages are non-synchronized and therefore may be transmitted at any time relative to the synchronized downlink timing by any mobile unit within the coverage area of the base station. The receiver in the base station must therefore continuously monitor the random access channels and search the signals received on the random access channels for predetermined sequences of symbols (sometimes referred to as the RACH preamble) in random access messages transmitted by mobile units. To make the search process feasible, the format of the random access messages must be standardized. For example, conventional random access messages in the Universal Mobile Telecommunication Services (UMTS) Long Term Evolution (LTE) system are transmitted in a subframe during a transmission time interval (TTI) of 1 ms in 1.08 MHz bandwidth. The random access messages subframe is divided into a 0.8 ms preamble and a 102.6 μs cyclic prefix that includes a copy of a portion of the sequence of symbols in the preamble. The remaining 97.4 μs in the transmission time interval is reserved as a guard time to reduce or prevent inter-symbol interference between different random access messages or shared data channels.
The sequence of symbols in the preamble may be formed from a basic Constant Amplitude Zero Auto Correlation (CAZAC) sequence. For example, according to TS 36.211, random access preambles xu,v(k) are formed from a CAZAC sequence generated by cyclic shifting of the u-th root Zadoff-Chu (ZC) sequence xu(k) of length NZC (NZC=839) by a multiples v of NCS, i.e.,xu,v(k)=xu((k+vNCS)mod N),  (1)where xu(k) is defined byxu(n)=e−jπun(n+1)/NCZ, n=0˜Ncz−1,The values of NCS for different configurations are given in the following table based on the agreement from Table 5.7.2-2 of TS36.211v8.2.0:
Ncs ValueNcs ConfigurationUnrestricted setRestricted set00151131821522318264223252638632467385584668959821076100119312812119158131672021427923715419—
FIG. 1 conceptually illustrates a conventional method of generating orthogonal sequences from an initial (or root) sequence. In FIG. 1, a set of orthogonal CAZAC sequences is generated using a cyclic shift of an initial sequence, CAZAC0(L). For example, a portion of the initial sequence CAZAC0(L) is copied from the right-hand side of the sequence shown in FIG. 1 to the left-hand side to form the cyclic prefix (CP) for the initial sequence CAZAC0(L). The next sequence CAZACQ(L) is formed by dropping the right-hand side portion of the initial sequence CAZAC0(L) and appending the cyclic prefix to the sequence CAZACQ(L). The cyclic prefix of the new sequence CAZACQ(L) is again formed by copying a portion of the right-hand side of the sequence CAZACQ(L) and appending it to the left-hand side of the sequence CAZACQ(L). Additional sequences CAZAC2Q-MQ(L) may be formed using the same algorithm. As long as the cyclic shift is longer than the maximum delay spread, the cyclically-shifted sequences are orthogonal.
The RACH receiver detects the random access signals by correlating the received signal with the reference signal xu(k) to identify possible peaks. Often, time domain correlation is implemented using FFT operations and frequency domain multiplication. Thus, the receiver needs to generate the frequency domain root sequence:
                                                        X              u                        ⁡                          (              k              )                                =                                                    ∑                                  k                  =                  0                                                                      N                    CZ                                    -                  1                                            ⁢                                                          ⁢                                                                    x                    u                                    ⁡                                      (                    n                    )                                                  ⁢                                                      ⅇ                                          j                      ⁢                                                                                          ⁢                      π                      ⁢                                                                                          ⁢                                              nk                        /                                                  N                          CZ                                                                                                      .                                                                          ⁢                  k                                                      =                          0              ∼                              Ncz                -                1                                                    ,                            (        2        )            A straightforward generation method requires performing an 839 point discrete Fourier transformed (DFT) to generate the frequency domain root sequence Xu(k). Since 839 is a prime number, this direct generation method is costly and requires complex hardware to implement. One alternative solution is to pre-generate and pre-store these sequences in the memory. However, this solution requires that a large amount of memory be allocated to store the pre-generated sequences.